A nipple newly inverting can be one of the early indications of cancer.
 More generally, cancerous growths tend to attach to surrounding
tissues and so can pull on the skin or milk ducts causing various
distortions such as depressions or "orange peel" or inverted nipple.
Benign lumps tend to be moveable and just produce a lump.

On the other hand some people's nipples invert routinely quite normally
(probably both of them) and this is not a problem - it is the change in
this behaviour, usually on one side only, that is of concern.

Tim Jackson